Welcome to the lovely field of Game Theory in mathematics. While yes, psychology plays quite a bit in this, it’s still considered a field of mathematics. So what is this stable marriage problem? I turned to Open AI’s Chat GPT to see how they would explain it and I thought they did a great job.
So in sorority recruitment, it would not place a woman in Chi Omega if both she preferred Alpha Gam & Alpha Gam preferred her more than the NMs who were placed there.
We also use this logic framework for Director matching. The metaphor of managers hiring through a hiring service might be the best analogy to use. Each VP is a manager who has jobs that they need to fill (the Directorships). Each job is a bit different.
So each manager reads through the resume each job applicant submits. Then managers rank the top applicants in order that they would prefer the candidates to work with them and submit this to the hiring service. Now each applicant can only accept 1 job. So each #1 choice applicant is offered the job. Some applicants will get more than one job offer. The applicants who get multiple job offers must pick the job they want the most and decline the rest of the offers.
In the next round, unfilled jobs move to their #2 choice applicant and offer those applicants the job. Again any applicant with multiple job offers in this round picks the one they want the most and declines the rest of the offers.
This procedure of offers/rejections repeats until all jobs are filled.
